//A super ugly number is a positive integer whose prime factors are in the array
// primes. 
//
// Given an integer n and an array of integers primes, return the nth super ugly
// number. 
//
// The nth super ugly number is guaranteed to fit in a 32-bit signed integer. 
//
// 
// Example 1: 
//
// 
//Input: n = 12, primes = [2,7,13,19]
//Output: 32
//Explanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 
//super ugly numbers given primes = [2,7,13,19].
// 
//
// Example 2: 
//
// 
//Input: n = 1, primes = [2,3,5]
//Output: 1
//Explanation: 1 has no prime factors, therefore all of its prime factors are in
// the array primes = [2,3,5].
// 
//
// 
// Constraints: 
//
// 
// 1 <= n <= 106 
// 1 <= primes.length <= 100 
// 2 <= primes[i] <= 1000 
// primes[i] is guaranteed to be a prime number. 
// All the values of primes are unique and sorted in ascending order. 
// 
// Related Topics 堆 数学 
// 👍 161 👎 0


package leetcode.editor.cn;

import java.util.Arrays;
import java.util.PriorityQueue;

//Java：Super Ugly Number
class P313SuperUglyNumber {
    public static void main(String[] args) {
        Solution solution = new P313SuperUglyNumber().new Solution();
        // TO TEST
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {
        public int nthSuperUglyNumber(int n, int[] primes) {
            int[] dp = new int[n + 1];
            int m = primes.length;
            int[] pointers = new int[m];
            int[] nums = new int[m];
            Arrays.fill(nums, 1);
            for (int i = 1; i <= n; i++) {
                int minNum = Arrays.stream(nums).min().getAsInt();
                dp[i] = minNum;
                for (int j = 0; j < m; j++) {
                    if (nums[j] == minNum) {
                        pointers[j]++;
                        nums[j] = dp[pointers[j]] * primes[j];
                    }
                }
            }
            return dp[n];
        }

        public int nthSuperUglyNumberArr(int n, int[] primes) {
            int m = primes.length;
            PriorityQueue<int[]> q = new PriorityQueue<>((a, b) -> a[0] - b[0]);
            for (int i = 0; i < m; i++) {
                q.add(new int[]{primes[i], i, 0});
            }
            int[] ans = new int[n];
            ans[0] = 1;
            for (int j = 1; j < n; ) {
                int[] poll = q.poll();
                int val = poll[0], i = poll[1], idx = poll[2];
                if (val != ans[j - 1]) ans[j++] = val;
                q.add(new int[]{ans[idx + 1] * primes[i], i, idx + 1});
            }
            return ans[n - 1];
        }
    }
//leetcode submit region end(Prohibit modification and deletion)


}